summaryrefslogtreecommitdiff
path: root/src/mesa/math/m_matrix.c
blob: 95a77e6a0842f37354dba43a44ffc5967a1ae832 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
/* $Id: m_matrix.c,v 1.16 2003/03/01 01:50:24 brianp Exp $ */

/*
 * Mesa 3-D graphics library
 * Version:  5.1
 *
 * Copyright (C) 1999-2003  Brian Paul   All Rights Reserved.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included
 * in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * BRIAN PAUL BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN
 * AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */


/*
 * Matrix operations
 *
 * NOTES:
 * 1. 4x4 transformation matrices are stored in memory in column major order.
 * 2. Points/vertices are to be thought of as column vectors.
 * 3. Transformation of a point p by a matrix M is: p' = M * p
 */

#include "glheader.h"
#include "imports.h"
#include "macros.h"
#include "imports.h"

#include "m_matrix.h"


static const char *types[] = {
   "MATRIX_GENERAL",
   "MATRIX_IDENTITY",
   "MATRIX_3D_NO_ROT",
   "MATRIX_PERSPECTIVE",
   "MATRIX_2D",
   "MATRIX_2D_NO_ROT",
   "MATRIX_3D"
};


static GLfloat Identity[16] = {
   1.0, 0.0, 0.0, 0.0,
   0.0, 1.0, 0.0, 0.0,
   0.0, 0.0, 1.0, 0.0,
   0.0, 0.0, 0.0, 1.0
};




/*
 * This matmul was contributed by Thomas Malik
 *
 * Perform a 4x4 matrix multiplication  (product = a x b).
 * Input:  a, b - matrices to multiply
 * Output:  product - product of a and b
 * WARNING: (product != b) assumed
 * NOTE:    (product == a) allowed
 *
 * KW: 4*16 = 64 muls
 */
#define A(row,col)  a[(col<<2)+row]
#define B(row,col)  b[(col<<2)+row]
#define P(row,col)  product[(col<<2)+row]

static void matmul4( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
   GLint i;
   for (i = 0; i < 4; i++) {
      const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
      P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0);
      P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1);
      P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2);
      P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3);
   }
}


/* Multiply two matrices known to occupy only the top three rows, such
 * as typical model matrices, and ortho matrices.
 */
static void matmul34( GLfloat *product, const GLfloat *a, const GLfloat *b )
{
   GLint i;
   for (i = 0; i < 3; i++) {
      const GLfloat ai0=A(i,0),  ai1=A(i,1),  ai2=A(i,2),  ai3=A(i,3);
      P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0);
      P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1);
      P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2);
      P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3;
   }
   P(3,0) = 0;
   P(3,1) = 0;
   P(3,2) = 0;
   P(3,3) = 1;
}


#undef A
#undef B
#undef P


/*
 * Multiply a matrix by an array of floats with known properties.
 */
static void matrix_multf( GLmatrix *mat, const GLfloat *m, GLuint flags )
{
   mat->flags |= (flags | MAT_DIRTY_TYPE | MAT_DIRTY_INVERSE);

   if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D))
      matmul34( mat->m, mat->m, m );
   else
      matmul4( mat->m, mat->m, m );
}


static void print_matrix_floats( const GLfloat m[16] )
{
   int i;
   for (i=0;i<4;i++) {
      _mesa_debug(NULL,"\t%f %f %f %f\n", m[i], m[4+i], m[8+i], m[12+i] );
   }
}

void
_math_matrix_print( const GLmatrix *m )
{
   _mesa_debug(NULL, "Matrix type: %s, flags: %x\n", types[m->type], m->flags);
   print_matrix_floats(m->m);
   _mesa_debug(NULL, "Inverse: \n");
   if (m->inv) {
      GLfloat prod[16];
      print_matrix_floats(m->inv);
      matmul4(prod, m->m, m->inv);
      _mesa_debug(NULL, "Mat * Inverse:\n");
      print_matrix_floats(prod);
   }
   else {
      _mesa_debug(NULL, "  - not available\n");
   }
}




#define SWAP_ROWS(a, b) { GLfloat *_tmp = a; (a)=(b); (b)=_tmp; }
#define MAT(m,r,c) (m)[(c)*4+(r)]

/*
 * Compute inverse of 4x4 transformation matrix.
 * Code contributed by Jacques Leroy jle@star.be
 * Return GL_TRUE for success, GL_FALSE for failure (singular matrix)
 */
static GLboolean invert_matrix_general( GLmatrix *mat )
{
   const GLfloat *m = mat->m;
   GLfloat *out = mat->inv;
   GLfloat wtmp[4][8];
   GLfloat m0, m1, m2, m3, s;
   GLfloat *r0, *r1, *r2, *r3;

   r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];

   r0[0] = MAT(m,0,0), r0[1] = MAT(m,0,1),
   r0[2] = MAT(m,0,2), r0[3] = MAT(m,0,3),
   r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,

   r1[0] = MAT(m,1,0), r1[1] = MAT(m,1,1),
   r1[2] = MAT(m,1,2), r1[3] = MAT(m,1,3),
   r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,

   r2[0] = MAT(m,2,0), r2[1] = MAT(m,2,1),
   r2[2] = MAT(m,2,2), r2[3] = MAT(m,2,3),
   r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,

   r3[0] = MAT(m,3,0), r3[1] = MAT(m,3,1),
   r3[2] = MAT(m,3,2), r3[3] = MAT(m,3,3),
   r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;

   /* choose pivot - or die */
   if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2);
   if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1);
   if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0);
   if (0.0 == r0[0])  return GL_FALSE;

   /* eliminate first variable     */
   m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0];
   s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s;
   s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s;
   s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s;
   s = r0[4];
   if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; }
   s = r0[5];
   if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; }
   s = r0[6];
   if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; }
   s = r0[7];
   if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; }

   /* choose pivot - or die */
   if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2);
   if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1);
   if (0.0 == r1[1])  return GL_FALSE;

   /* eliminate second variable */
   m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1];
   r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2];
   r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3];
   s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; }
   s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; }
   s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; }
   s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; }

   /* choose pivot - or die */
   if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2);
   if (0.0 == r2[2])  return GL_FALSE;

   /* eliminate third variable */
   m3 = r3[2]/r2[2];
   r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
   r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6],
   r3[7] -= m3 * r2[7];

   /* last check */
   if (0.0 == r3[3]) return GL_FALSE;

   s = 1.0F/r3[3];             /* now back substitute row 3 */
   r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s;

   m2 = r2[3];                 /* now back substitute row 2 */
   s  = 1.0F/r2[2];
   r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
   r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
   m1 = r1[3];
   r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
   r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
   m0 = r0[3];
   r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
   r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;

   m1 = r1[2];                 /* now back substitute row 1 */
   s  = 1.0F/r1[1];
   r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
   r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
   m0 = r0[2];
   r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
   r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;

   m0 = r0[1];                 /* now back substitute row 0 */
   s  = 1.0F/r0[0];
   r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
   r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);

   MAT(out,0,0) = r0[4]; MAT(out,0,1) = r0[5],
   MAT(out,0,2) = r0[6]; MAT(out,0,3) = r0[7],
   MAT(out,1,0) = r1[4]; MAT(out,1,1) = r1[5],
   MAT(out,1,2) = r1[6]; MAT(out,1,3) = r1[7],
   MAT(out,2,0) = r2[4]; MAT(out,2,1) = r2[5],
   MAT(out,2,2) = r2[6]; MAT(out,2,3) = r2[7],
   MAT(out,3,0) = r3[4]; MAT(out,3,1) = r3[5],
   MAT(out,3,2) = r3[6]; MAT(out,3,3) = r3[7];

   return GL_TRUE;
}
#undef SWAP_ROWS


/* Adapted from graphics gems II.
 */
static GLboolean invert_matrix_3d_general( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;
   GLfloat pos, neg, t;
   GLfloat det;

   /* Calculate the determinant of upper left 3x3 submatrix and
    * determine if the matrix is singular.
    */
   pos = neg = 0.0;
   t =  MAT(in,0,0) * MAT(in,1,1) * MAT(in,2,2);
   if (t >= 0.0) pos += t; else neg += t;

   t =  MAT(in,1,0) * MAT(in,2,1) * MAT(in,0,2);
   if (t >= 0.0) pos += t; else neg += t;

   t =  MAT(in,2,0) * MAT(in,0,1) * MAT(in,1,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,2,0) * MAT(in,1,1) * MAT(in,0,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,1,0) * MAT(in,0,1) * MAT(in,2,2);
   if (t >= 0.0) pos += t; else neg += t;

   t = -MAT(in,0,0) * MAT(in,2,1) * MAT(in,1,2);
   if (t >= 0.0) pos += t; else neg += t;

   det = pos + neg;

   if (det*det < 1e-25)
      return GL_FALSE;

   det = 1.0F / det;
   MAT(out,0,0) = (  (MAT(in,1,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,1,2) )*det);
   MAT(out,0,1) = (- (MAT(in,0,1)*MAT(in,2,2) - MAT(in,2,1)*MAT(in,0,2) )*det);
   MAT(out,0,2) = (  (MAT(in,0,1)*MAT(in,1,2) - MAT(in,1,1)*MAT(in,0,2) )*det);
   MAT(out,1,0) = (- (MAT(in,1,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,1,2) )*det);
   MAT(out,1,1) = (  (MAT(in,0,0)*MAT(in,2,2) - MAT(in,2,0)*MAT(in,0,2) )*det);
   MAT(out,1,2) = (- (MAT(in,0,0)*MAT(in,1,2) - MAT(in,1,0)*MAT(in,0,2) )*det);
   MAT(out,2,0) = (  (MAT(in,1,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,1,1) )*det);
   MAT(out,2,1) = (- (MAT(in,0,0)*MAT(in,2,1) - MAT(in,2,0)*MAT(in,0,1) )*det);
   MAT(out,2,2) = (  (MAT(in,0,0)*MAT(in,1,1) - MAT(in,1,0)*MAT(in,0,1) )*det);

   /* Do the translation part */
   MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
		     MAT(in,1,3) * MAT(out,0,1) +
		     MAT(in,2,3) * MAT(out,0,2) );
   MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
		     MAT(in,1,3) * MAT(out,1,1) +
		     MAT(in,2,3) * MAT(out,1,2) );
   MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
		     MAT(in,1,3) * MAT(out,2,1) +
		     MAT(in,2,3) * MAT(out,2,2) );

   return GL_TRUE;
}


static GLboolean invert_matrix_3d( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (!TEST_MAT_FLAGS(mat, MAT_FLAGS_ANGLE_PRESERVING)) {
      return invert_matrix_3d_general( mat );
   }

   if (mat->flags & MAT_FLAG_UNIFORM_SCALE) {
      GLfloat scale = (MAT(in,0,0) * MAT(in,0,0) +
                       MAT(in,0,1) * MAT(in,0,1) +
                       MAT(in,0,2) * MAT(in,0,2));

      if (scale == 0.0)
         return GL_FALSE;

      scale = 1.0F / scale;

      /* Transpose and scale the 3 by 3 upper-left submatrix. */
      MAT(out,0,0) = scale * MAT(in,0,0);
      MAT(out,1,0) = scale * MAT(in,0,1);
      MAT(out,2,0) = scale * MAT(in,0,2);
      MAT(out,0,1) = scale * MAT(in,1,0);
      MAT(out,1,1) = scale * MAT(in,1,1);
      MAT(out,2,1) = scale * MAT(in,1,2);
      MAT(out,0,2) = scale * MAT(in,2,0);
      MAT(out,1,2) = scale * MAT(in,2,1);
      MAT(out,2,2) = scale * MAT(in,2,2);
   }
   else if (mat->flags & MAT_FLAG_ROTATION) {
      /* Transpose the 3 by 3 upper-left submatrix. */
      MAT(out,0,0) = MAT(in,0,0);
      MAT(out,1,0) = MAT(in,0,1);
      MAT(out,2,0) = MAT(in,0,2);
      MAT(out,0,1) = MAT(in,1,0);
      MAT(out,1,1) = MAT(in,1,1);
      MAT(out,2,1) = MAT(in,1,2);
      MAT(out,0,2) = MAT(in,2,0);
      MAT(out,1,2) = MAT(in,2,1);
      MAT(out,2,2) = MAT(in,2,2);
   }
   else {
      /* pure translation */
      MEMCPY( out, Identity, sizeof(Identity) );
      MAT(out,0,3) = - MAT(in,0,3);
      MAT(out,1,3) = - MAT(in,1,3);
      MAT(out,2,3) = - MAT(in,2,3);
      return GL_TRUE;
   }

   if (mat->flags & MAT_FLAG_TRANSLATION) {
      /* Do the translation part */
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0) +
			MAT(in,1,3) * MAT(out,0,1) +
			MAT(in,2,3) * MAT(out,0,2) );
      MAT(out,1,3) = - (MAT(in,0,3) * MAT(out,1,0) +
			MAT(in,1,3) * MAT(out,1,1) +
			MAT(in,2,3) * MAT(out,1,2) );
      MAT(out,2,3) = - (MAT(in,0,3) * MAT(out,2,0) +
			MAT(in,1,3) * MAT(out,2,1) +
			MAT(in,2,3) * MAT(out,2,2) );
   }
   else {
      MAT(out,0,3) = MAT(out,1,3) = MAT(out,2,3) = 0.0;
   }

   return GL_TRUE;
}



static GLboolean invert_matrix_identity( GLmatrix *mat )
{
   MEMCPY( mat->inv, Identity, sizeof(Identity) );
   return GL_TRUE;
}


static GLboolean invert_matrix_3d_no_rot( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0 || MAT(in,2,2) == 0 )
      return GL_FALSE;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   MAT(out,0,0) = 1.0F / MAT(in,0,0);
   MAT(out,1,1) = 1.0F / MAT(in,1,1);
   MAT(out,2,2) = 1.0F / MAT(in,2,2);

   if (mat->flags & MAT_FLAG_TRANSLATION) {
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
      MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
      MAT(out,2,3) = - (MAT(in,2,3) * MAT(out,2,2));
   }

   return GL_TRUE;
}


static GLboolean invert_matrix_2d_no_rot( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,0,0) == 0 || MAT(in,1,1) == 0)
      return GL_FALSE;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );
   MAT(out,0,0) = 1.0F / MAT(in,0,0);
   MAT(out,1,1) = 1.0F / MAT(in,1,1);

   if (mat->flags & MAT_FLAG_TRANSLATION) {
      MAT(out,0,3) = - (MAT(in,0,3) * MAT(out,0,0));
      MAT(out,1,3) = - (MAT(in,1,3) * MAT(out,1,1));
   }

   return GL_TRUE;
}


#if 0
/* broken */
static GLboolean invert_matrix_perspective( GLmatrix *mat )
{
   const GLfloat *in = mat->m;
   GLfloat *out = mat->inv;

   if (MAT(in,2,3) == 0)
      return GL_FALSE;

   MEMCPY( out, Identity, 16 * sizeof(GLfloat) );

   MAT(out,0,0) = 1.0F / MAT(in,0,0);
   MAT(out,1,1) = 1.0F / MAT(in,1,1);

   MAT(out,0,3) = MAT(in,0,2);
   MAT(out,1,3) = MAT(in,1,2);

   MAT(out,2,2) = 0;
   MAT(out,2,3) = -1;

   MAT(out,3,2) = 1.0F / MAT(in,2,3);
   MAT(out,3,3) = MAT(in,2,2) * MAT(out,3,2);

   return GL_TRUE;
}
#endif


typedef GLboolean (*inv_mat_func)( GLmatrix *mat );


static inv_mat_func inv_mat_tab[7] = {
   invert_matrix_general,
   invert_matrix_identity,
   invert_matrix_3d_no_rot,
#if 0
   /* Don't use this function for now - it fails when the projection matrix
    * is premultiplied by a translation (ala Chromium's tilesort SPU).
    */
   invert_matrix_perspective,
#else
   invert_matrix_general,
#endif
   invert_matrix_3d,		/* lazy! */
   invert_matrix_2d_no_rot,
   invert_matrix_3d
};


static GLboolean matrix_invert( GLmatrix *mat )
{
   if (inv_mat_tab[mat->type](mat)) {
      mat->flags &= ~MAT_FLAG_SINGULAR;
      return GL_TRUE;
   } else {
      mat->flags |= MAT_FLAG_SINGULAR;
      MEMCPY( mat->inv, Identity, sizeof(Identity) );
      return GL_FALSE;
   }
}






/*
 * Generate a 4x4 transformation matrix from glRotate parameters, and
 * postmultiply the input matrix by it.
 * This function contributed by Erich Boleyn (erich@uruk.org).
 * Optimizatios contributed by Rudolf Opalla (rudi@khm.de).
 */
void
_math_matrix_rotate( GLmatrix *mat,
		     GLfloat angle, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c, s, c;
   GLfloat m[16];
   GLboolean optimized;

   s = (GLfloat) sin( angle * DEG2RAD );
   c = (GLfloat) cos( angle * DEG2RAD );

   MEMCPY(m, Identity, sizeof(GLfloat)*16);
   optimized = GL_FALSE;

#define M(row,col)  m[col*4+row]

   if (x == 0.0F) {
      if (y == 0.0F) {
         if (z != 0.0F) {
            optimized = GL_TRUE;
            /* rotate only around z-axis */
            M(0,0) = c;
            M(1,1) = c;
            if (z < 0.0F) {
               M(0,1) = s;
               M(1,0) = -s;
            }
            else {
               M(0,1) = -s;
               M(1,0) = s;
            }
         }
      }
      else if (z == 0.0F) {
         optimized = GL_TRUE;
         /* rotate only around y-axis */
         M(0,0) = c;
         M(2,2) = c;
         if (y < 0.0F) {
            M(0,2) = -s;
            M(2,0) = s;
         }
         else {
            M(0,2) = s;
            M(2,0) = -s;
         }
      }
   }
   else if (y == 0.0F) {
      if (z == 0.0F) {
         optimized = GL_TRUE;
         /* rotate only around x-axis */
         M(1,1) = c;
         M(2,2) = c;
         if (x < 0.0F) {
            M(1,2) = s;
            M(2,1) = -s;
         }
         else {
            M(1,2) = -s;
            M(2,1) = s;
         }
      }
   }

   if (!optimized) {
      const GLfloat mag = SQRTF(x * x + y * y + z * z);

      if (mag <= 1.0e-4) {
         /* no rotation, leave mat as-is */
         return;
      }

      x /= mag;
      y /= mag;
      z /= mag;


      /*
       *     Arbitrary axis rotation matrix.
       *
       *  This is composed of 5 matrices, Rz, Ry, T, Ry', Rz', multiplied
       *  like so:  Rz * Ry * T * Ry' * Rz'.  T is the final rotation
       *  (which is about the X-axis), and the two composite transforms
       *  Ry' * Rz' and Rz * Ry are (respectively) the rotations necessary
       *  from the arbitrary axis to the X-axis then back.  They are
       *  all elementary rotations.
       *
       *  Rz' is a rotation about the Z-axis, to bring the axis vector
       *  into the x-z plane.  Then Ry' is applied, rotating about the
       *  Y-axis to bring the axis vector parallel with the X-axis.  The
       *  rotation about the X-axis is then performed.  Ry and Rz are
       *  simply the respective inverse transforms to bring the arbitrary
       *  axis back to it's original orientation.  The first transforms
       *  Rz' and Ry' are considered inverses, since the data from the
       *  arbitrary axis gives you info on how to get to it, not how
       *  to get away from it, and an inverse must be applied.
       *
       *  The basic calculation used is to recognize that the arbitrary
       *  axis vector (x, y, z), since it is of unit length, actually
       *  represents the sines and cosines of the angles to rotate the
       *  X-axis to the same orientation, with theta being the angle about
       *  Z and phi the angle about Y (in the order described above)
       *  as follows:
       *
       *  cos ( theta ) = x / sqrt ( 1 - z^2 )
       *  sin ( theta ) = y / sqrt ( 1 - z^2 )
       *
       *  cos ( phi ) = sqrt ( 1 - z^2 )
       *  sin ( phi ) = z
       *
       *  Note that cos ( phi ) can further be inserted to the above
       *  formulas:
       *
       *  cos ( theta ) = x / cos ( phi )
       *  sin ( theta ) = y / sin ( phi )
       *
       *  ...etc.  Because of those relations and the standard trigonometric
       *  relations, it is pssible to reduce the transforms down to what
       *  is used below.  It may be that any primary axis chosen will give the
       *  same results (modulo a sign convention) using thie method.
       *
       *  Particularly nice is to notice that all divisions that might
       *  have caused trouble when parallel to certain planes or
       *  axis go away with care paid to reducing the expressions.
       *  After checking, it does perform correctly under all cases, since
       *  in all the cases of division where the denominator would have
       *  been zero, the numerator would have been zero as well, giving
       *  the expected result.
       */

      xx = x * x;
      yy = y * y;
      zz = z * z;
      xy = x * y;
      yz = y * z;
      zx = z * x;
      xs = x * s;
      ys = y * s;
      zs = z * s;
      one_c = 1.0F - c;

      /* We already hold the identity-matrix so we can skip some statements */
      M(0,0) = (one_c * xx) + c;
      M(0,1) = (one_c * xy) - zs;
      M(0,2) = (one_c * zx) + ys;
/*    M(0,3) = 0.0F; */

      M(1,0) = (one_c * xy) + zs;
      M(1,1) = (one_c * yy) + c;
      M(1,2) = (one_c * yz) - xs;
/*    M(1,3) = 0.0F; */

      M(2,0) = (one_c * zx) - ys;
      M(2,1) = (one_c * yz) + xs;
      M(2,2) = (one_c * zz) + c;
/*    M(2,3) = 0.0F; */

/*
      M(3,0) = 0.0F;
      M(3,1) = 0.0F;
      M(3,2) = 0.0F;
      M(3,3) = 1.0F;
*/
   }
#undef M

   matrix_multf( mat, m, MAT_FLAG_ROTATION );
}



void
_math_matrix_frustum( GLmatrix *mat,
		      GLfloat left, GLfloat right,
		      GLfloat bottom, GLfloat top,
		      GLfloat nearval, GLfloat farval )
{
   GLfloat x, y, a, b, c, d;
   GLfloat m[16];

   x = (2.0F*nearval) / (right-left);
   y = (2.0F*nearval) / (top-bottom);
   a = (right+left) / (right-left);
   b = (top+bottom) / (top-bottom);
   c = -(farval+nearval) / ( farval-nearval);
   d = -(2.0F*farval*nearval) / (farval-nearval);  /* error? */

#define M(row,col)  m[col*4+row]
   M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = a;      M(0,3) = 0.0F;
   M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = b;      M(1,3) = 0.0F;
   M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = c;      M(2,3) = d;
   M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = -1.0F;  M(3,3) = 0.0F;
#undef M

   matrix_multf( mat, m, MAT_FLAG_PERSPECTIVE );
}

void
_math_matrix_ortho( GLmatrix *mat,
		    GLfloat left, GLfloat right,
		    GLfloat bottom, GLfloat top,
		    GLfloat nearval, GLfloat farval )
{
   GLfloat x, y, z;
   GLfloat tx, ty, tz;
   GLfloat m[16];

   x = 2.0F / (right-left);
   y = 2.0F / (top-bottom);
   z = -2.0F / (farval-nearval);
   tx = -(right+left) / (right-left);
   ty = -(top+bottom) / (top-bottom);
   tz = -(farval+nearval) / (farval-nearval);

#define M(row,col)  m[col*4+row]
   M(0,0) = x;     M(0,1) = 0.0F;  M(0,2) = 0.0F;  M(0,3) = tx;
   M(1,0) = 0.0F;  M(1,1) = y;     M(1,2) = 0.0F;  M(1,3) = ty;
   M(2,0) = 0.0F;  M(2,1) = 0.0F;  M(2,2) = z;     M(2,3) = tz;
   M(3,0) = 0.0F;  M(3,1) = 0.0F;  M(3,2) = 0.0F;  M(3,3) = 1.0F;
#undef M

   matrix_multf( mat, m, (MAT_FLAG_GENERAL_SCALE|MAT_FLAG_TRANSLATION));
}


#define ZERO(x) (1<<x)
#define ONE(x)  (1<<(x+16))

#define MASK_NO_TRX      (ZERO(12) | ZERO(13) | ZERO(14))
#define MASK_NO_2D_SCALE ( ONE(0)  | ONE(5))

#define MASK_IDENTITY    ( ONE(0)  | ZERO(4)  | ZERO(8)  | ZERO(12) |\
			  ZERO(1)  |  ONE(5)  | ZERO(9)  | ZERO(13) |\
			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_2D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
			  ZERO(1)  |            ZERO(9)  |           \
			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_2D          (                      ZERO(8)  |           \
			                        ZERO(9)  |           \
			  ZERO(2)  | ZERO(6)  |  ONE(10) | ZERO(14) |\
			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )


#define MASK_3D_NO_ROT   (           ZERO(4)  | ZERO(8)  |           \
			  ZERO(1)  |            ZERO(9)  |           \
			  ZERO(2)  | ZERO(6)  |                      \
			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )

#define MASK_3D          (                                           \
			                                             \
			                                             \
			  ZERO(3)  | ZERO(7)  | ZERO(11) |  ONE(15) )


#define MASK_PERSPECTIVE (           ZERO(4)  |            ZERO(12) |\
			  ZERO(1)  |                       ZERO(13) |\
			  ZERO(2)  | ZERO(6)  |                      \
			  ZERO(3)  | ZERO(7)  |            ZERO(15) )

#define SQ(x) ((x)*(x))

/* Determine type and flags from scratch.  This is expensive enough to
 * only want to do it once.
 */
static void analyse_from_scratch( GLmatrix *mat )
{
   const GLfloat *m = mat->m;
   GLuint mask = 0;
   GLuint i;

   for (i = 0 ; i < 16 ; i++) {
      if (m[i] == 0.0) mask |= (1<<i);
   }

   if (m[0] == 1.0F) mask |= (1<<16);
   if (m[5] == 1.0F) mask |= (1<<21);
   if (m[10] == 1.0F) mask |= (1<<26);
   if (m[15] == 1.0F) mask |= (1<<31);

   mat->flags &= ~MAT_FLAGS_GEOMETRY;

   /* Check for translation - no-one really cares
    */
   if ((mask & MASK_NO_TRX) != MASK_NO_TRX)
      mat->flags |= MAT_FLAG_TRANSLATION;

   /* Do the real work
    */
   if (mask == (GLuint) MASK_IDENTITY) {
      mat->type = MATRIX_IDENTITY;
   }
   else if ((mask & MASK_2D_NO_ROT) == (GLuint) MASK_2D_NO_ROT) {
      mat->type = MATRIX_2D_NO_ROT;

      if ((mask & MASK_NO_2D_SCALE) != MASK_NO_2D_SCALE)
	 mat->flags = MAT_FLAG_GENERAL_SCALE;
   }
   else if ((mask & MASK_2D) == (GLuint) MASK_2D) {
      GLfloat mm = DOT2(m, m);
      GLfloat m4m4 = DOT2(m+4,m+4);
      GLfloat mm4 = DOT2(m,m+4);

      mat->type = MATRIX_2D;

      /* Check for scale */
      if (SQ(mm-1) > SQ(1e-6) ||
	  SQ(m4m4-1) > SQ(1e-6))
	 mat->flags |= MAT_FLAG_GENERAL_SCALE;

      /* Check for rotation */
      if (SQ(mm4) > SQ(1e-6))
	 mat->flags |= MAT_FLAG_GENERAL_3D;
      else
	 mat->flags |= MAT_FLAG_ROTATION;

   }
   else if ((mask & MASK_3D_NO_ROT) == (GLuint) MASK_3D_NO_ROT) {
      mat->type = MATRIX_3D_NO_ROT;

      /* Check for scale */
      if (SQ(m[0]-m[5]) < SQ(1e-6) &&
	  SQ(m[0]-m[10]) < SQ(1e-6)) {
	 if (SQ(m[0]-1.0) > SQ(1e-6)) {
	    mat->flags |= MAT_FLAG_UNIFORM_SCALE;
         }
      }
      else {
	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
      }
   }
   else if ((mask & MASK_3D) == (GLuint) MASK_3D) {
      GLfloat c1 = DOT3(m,m);
      GLfloat c2 = DOT3(m+4,m+4);
      GLfloat c3 = DOT3(m+8,m+8);
      GLfloat d1 = DOT3(m, m+4);
      GLfloat cp[3];

      mat->type = MATRIX_3D;

      /* Check for scale */
      if (SQ(c1-c2) < SQ(1e-6) && SQ(c1-c3) < SQ(1e-6)) {
	 if (SQ(c1-1.0) > SQ(1e-6))
	    mat->flags |= MAT_FLAG_UNIFORM_SCALE;
	 /* else no scale at all */
      }
      else {
	 mat->flags |= MAT_FLAG_GENERAL_SCALE;
      }

      /* Check for rotation */
      if (SQ(d1) < SQ(1e-6)) {
	 CROSS3( cp, m, m+4 );
	 SUB_3V( cp, cp, (m+8) );
	 if (LEN_SQUARED_3FV(cp) < SQ(1e-6))
	    mat->flags |= MAT_FLAG_ROTATION;
	 else
	    mat->flags |= MAT_FLAG_GENERAL_3D;
      }
      else {
	 mat->flags |= MAT_FLAG_GENERAL_3D; /* shear, etc */
      }
   }
   else if ((mask & MASK_PERSPECTIVE) == MASK_PERSPECTIVE && m[11]==-1.0F) {
      mat->type = MATRIX_PERSPECTIVE;
      mat->flags |= MAT_FLAG_GENERAL;
   }
   else {
      mat->type = MATRIX_GENERAL;
      mat->flags |= MAT_FLAG_GENERAL;
   }
}


/* Analyse a matrix given that its flags are accurate - this is the
 * more common operation, hopefully.
 */
static void analyse_from_flags( GLmatrix *mat )
{
   const GLfloat *m = mat->m;

   if (TEST_MAT_FLAGS(mat, 0)) {
      mat->type = MATRIX_IDENTITY;
   }
   else if (TEST_MAT_FLAGS(mat, (MAT_FLAG_TRANSLATION |
				 MAT_FLAG_UNIFORM_SCALE |
				 MAT_FLAG_GENERAL_SCALE))) {
      if ( m[10]==1.0F && m[14]==0.0F ) {
	 mat->type = MATRIX_2D_NO_ROT;
      }
      else {
	 mat->type = MATRIX_3D_NO_ROT;
      }
   }
   else if (TEST_MAT_FLAGS(mat, MAT_FLAGS_3D)) {
      if (                                 m[ 8]==0.0F
            &&                             m[ 9]==0.0F
            && m[2]==0.0F && m[6]==0.0F && m[10]==1.0F && m[14]==0.0F) {
	 mat->type = MATRIX_2D;
      }
      else {
	 mat->type = MATRIX_3D;
      }
   }
   else if (                 m[4]==0.0F                 && m[12]==0.0F
            && m[1]==0.0F                               && m[13]==0.0F
            && m[2]==0.0F && m[6]==0.0F
            && m[3]==0.0F && m[7]==0.0F && m[11]==-1.0F && m[15]==0.0F) {
      mat->type = MATRIX_PERSPECTIVE;
   }
   else {
      mat->type = MATRIX_GENERAL;
   }
}


void
_math_matrix_analyse( GLmatrix *mat )
{
   if (mat->flags & MAT_DIRTY_TYPE) {
      if (mat->flags & MAT_DIRTY_FLAGS)
	 analyse_from_scratch( mat );
      else
	 analyse_from_flags( mat );
   }

   if (mat->inv && (mat->flags & MAT_DIRTY_INVERSE)) {
      matrix_invert( mat );
   }

   mat->flags &= ~(MAT_DIRTY_FLAGS|
		   MAT_DIRTY_TYPE|
		   MAT_DIRTY_INVERSE);
}


void
_math_matrix_copy( GLmatrix *to, const GLmatrix *from )
{
   MEMCPY( to->m, from->m, sizeof(Identity) );
   to->flags = from->flags;
   to->type = from->type;

   if (to->inv != 0) {
      if (from->inv == 0) {
	 matrix_invert( to );
      }
      else {
	 MEMCPY(to->inv, from->inv, sizeof(GLfloat)*16);
      }
   }
}


void
_math_matrix_scale( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat *m = mat->m;
   m[0] *= x;   m[4] *= y;   m[8]  *= z;
   m[1] *= x;   m[5] *= y;   m[9]  *= z;
   m[2] *= x;   m[6] *= y;   m[10] *= z;
   m[3] *= x;   m[7] *= y;   m[11] *= z;

   if (fabs(x - y) < 1e-8 && fabs(x - z) < 1e-8)
      mat->flags |= MAT_FLAG_UNIFORM_SCALE;
   else
      mat->flags |= MAT_FLAG_GENERAL_SCALE;

   mat->flags |= (MAT_DIRTY_TYPE |
		  MAT_DIRTY_INVERSE);
}


void
_math_matrix_translate( GLmatrix *mat, GLfloat x, GLfloat y, GLfloat z )
{
   GLfloat *m = mat->m;
   m[12] = m[0] * x + m[4] * y + m[8]  * z + m[12];
   m[13] = m[1] * x + m[5] * y + m[9]  * z + m[13];
   m[14] = m[2] * x + m[6] * y + m[10] * z + m[14];
   m[15] = m[3] * x + m[7] * y + m[11] * z + m[15];

   mat->flags |= (MAT_FLAG_TRANSLATION |
		  MAT_DIRTY_TYPE |
		  MAT_DIRTY_INVERSE);
}


void
_math_matrix_loadf( GLmatrix *mat, const GLfloat *m )
{
   MEMCPY( mat->m, m, 16*sizeof(GLfloat) );
   mat->flags = (MAT_FLAG_GENERAL | MAT_DIRTY);
}

void
_math_matrix_ctr( GLmatrix *m )
{
   m->m = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
   if (m->m)
      MEMCPY( m->m, Identity, sizeof(Identity) );
   m->inv = NULL;
   m->type = MATRIX_IDENTITY;
   m->flags = 0;
}

void
_math_matrix_dtr( GLmatrix *m )
{
   if (m->m) {
      ALIGN_FREE( m->m );
      m->m = NULL;
   }
   if (m->inv) {
      ALIGN_FREE( m->inv );
      m->inv = NULL;
   }
}


void
_math_matrix_alloc_inv( GLmatrix *m )
{
   if (!m->inv) {
      m->inv = (GLfloat *) ALIGN_MALLOC( 16 * sizeof(GLfloat), 16 );
      if (m->inv)
         MEMCPY( m->inv, Identity, 16 * sizeof(GLfloat) );
   }
}


void
_math_matrix_mul_matrix( GLmatrix *dest, const GLmatrix *a, const GLmatrix *b )
{
   dest->flags = (a->flags |
		  b->flags |
		  MAT_DIRTY_TYPE |
		  MAT_DIRTY_INVERSE);

   if (TEST_MAT_FLAGS(dest, MAT_FLAGS_3D))
      matmul34( dest->m, a->m, b->m );
   else
      matmul4( dest->m, a->m, b->m );
}


void
_math_matrix_mul_floats( GLmatrix *dest, const GLfloat *m )
{
   dest->flags |= (MAT_FLAG_GENERAL |
		   MAT_DIRTY_TYPE |
		   MAT_DIRTY_INVERSE);

   matmul4( dest->m, dest->m, m );
}

void
_math_matrix_set_identity( GLmatrix *mat )
{
   MEMCPY( mat->m, Identity, 16*sizeof(GLfloat) );

   if (mat->inv)
      MEMCPY( mat->inv, Identity, 16*sizeof(GLfloat) );

   mat->type = MATRIX_IDENTITY;
   mat->flags &= ~(MAT_DIRTY_FLAGS|
		   MAT_DIRTY_TYPE|
		   MAT_DIRTY_INVERSE);
}



void
_math_transposef( GLfloat to[16], const GLfloat from[16] )
{
   to[0] = from[0];
   to[1] = from[4];
   to[2] = from[8];
   to[3] = from[12];
   to[4] = from[1];
   to[5] = from[5];
   to[6] = from[9];
   to[7] = from[13];
   to[8] = from[2];
   to[9] = from[6];
   to[10] = from[10];
   to[11] = from[14];
   to[12] = from[3];
   to[13] = from[7];
   to[14] = from[11];
   to[15] = from[15];
}


void
_math_transposed( GLdouble to[16], const GLdouble from[16] )
{
   to[0] = from[0];
   to[1] = from[4];
   to[2] = from[8];
   to[3] = from[12];
   to[4] = from[1];
   to[5] = from[5];
   to[6] = from[9];
   to[7] = from[13];
   to[8] = from[2];
   to[9] = from[6];
   to[10] = from[10];
   to[11] = from[14];
   to[12] = from[3];
   to[13] = from[7];
   to[14] = from[11];
   to[15] = from[15];
}

void
_math_transposefd( GLfloat to[16], const GLdouble from[16] )
{
   to[0] = (GLfloat) from[0];
   to[1] = (GLfloat) from[4];
   to[2] = (GLfloat) from[8];
   to[3] = (GLfloat) from[12];
   to[4] = (GLfloat) from[1];
   to[5] = (GLfloat) from[5];
   to[6] = (GLfloat) from[9];
   to[7] = (GLfloat) from[13];
   to[8] = (GLfloat) from[2];
   to[9] = (GLfloat) from[6];
   to[10] = (GLfloat) from[10];
   to[11] = (GLfloat) from[14];
   to[12] = (GLfloat) from[3];
   to[13] = (GLfloat) from[7];
   to[14] = (GLfloat) from[11];
   to[15] = (GLfloat) from[15];
}